Classification of traveling waves for a quadratic Szeg{ö} equation

Abstract

We give a complete classification of the traveling waves of the following quadratic Szeg{ö} equation : $i\partial \_tu=2J\Pi (|u{|}^2)+\bar{J}{u}^2,u(0,\cdot )=u\_0$, and we show that they are given by two families of rational functions, one of which is generated by a stable ground state. We prove that the other branch is orbitally unstable.